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How to Open Students' Mathematical Thinking
Confucius said, "Knowing is not as good as being kind, and being kind is not as good as being happy." Here, interest is the driving force of thinking. When students are interested in something, they are focused, curious and quick-thinking. Especially in the teaching of lower grades, because students are young, flexible and diverse teaching methods are adopted to make students learn interesting and have fun, which is conducive to stimulating students' thirst for knowledge and consolidating what they have learned. In teaching, I start with the word "interest" and present the teaching content in various ways, so that students can feel the fun of learning mathematics, and then activate their thinking and change their learning methods, so that they can participate in the whole process of learning with a positive attitude. Now I will tell my own experience as follows:

First, cleverly set the situation to create a strong classroom learning atmosphere

The so-called situation is the learning atmosphere created to achieve the purpose of learning and stimulate students' interest and curiosity. Pupils generally have a curious and inquisitive psychology. Vivid situations can often make students' mental state quickly change from inhibition to excitement, and at the same time make students have their own needs for learning knowledge, thus arousing their desire for learning.

1, turn static into dynamic, and stimulate students' interest.

When you count to 8 or 9, the children have learned logarithm. Then, starting with the order, cardinal number and ordinal number of numbers, students certainly don't like to hear it. So here I created a scene of small animals participating in the Tour, which appeared in the animation form of computer courseware: seven small animals gathered on the beautiful prairie, and they were going to participate in the Tour. "Wait for me" A big cow also ran into the picture. How many animals are there now? A vivid picture appeared in front of the students, and their eyes were attracted, so the small animal contest began with the participation of the students. In this class, the multimedia computer makes the static 8 and 9 move, and presents the knowledge of the source, size and composition of 8 and 9 in a dynamic way, which makes the abstract teaching content vivid and intuitive, and students soon have the interest in learning and the desire for knowledge.

2. Create a story kingdom to stimulate students' interest.

Students in the lower grades of primary school love to listen to stories. According to this psychological characteristic of students, I often combine the mathematical knowledge in books with real life and make up stories to attract students' attention, stimulate their interest in learning and inspire their thinking, so as to achieve better teaching results. In the lesson "Compare", I started with a fairy tale that children like to hear: "The wolf wanted to eat the pig, so he blew away the straw house they built and burned down the wooden house. Finally, three little pigs built a stone house. The wolf couldn't help it this time, but he was unwilling. What can he do? Three little pigs decided to help the little rabbit build a stone house. Look, they are moving materials together. Show me the picture of pigs helping rabbits build houses. " What can you see from the picture? "Children have changed from listening to stories to seriously reading stories, actively thinking about stories, with high interest and active thinking. Through observation and comparison, they understand the meanings of "more", "less" and "as much" and the methods of comparison. Children like these stories because they are close to their world; Children are willing to learn in stories because stories are affectionate, which can make children integrate into them and experience the endless fun of mathematics.

3. Use the materials in life to stimulate students' interest.

Paying attention to the cultivation of application consciousness and practical ability is one of the focuses of current mathematics curriculum reform. Active activities are an important way for children to acquire knowledge and develop their abilities. The first-year students have less knowledge of mathematics and narrow contact with society. By connecting with practice, we can solve the problems in students' lives, so that students can feel that there is mathematics everywhere in their lives, and they will be more interested in learning. If we say "classification", we first present a picture of life, that is, Xiao Ming's messy room: toys on the bed, lying shoes, books, socks and hats, schoolbags opened on the chair, skipping rope, basketball, scarves and so on. The room is the most familiar place in a child's life. As soon as they saw the pictures, they felt the clutter in the room, and they had the desire to help Xiao Ming tidy up the room, thus realizing the importance of classification. This kind of teaching content is familiar to students and easy to learn. Many people can come up with different classification methods with great interest according to their own life experiences.

4, learning in the game, entertaining.

First-year students have just left kindergarten and are not familiar with school life and learning methods. According to their age characteristics, psychological characteristics and study habits, their unique learning methods are determined-playing middle school and playing middle school. When teaching "Composition and Decomposition of Numbers", I designed a game of "Finding Friends": the children who participated in the game put on digital cards and found friends with each other along with the melody of "Finding, Finding and Finding a Good Friend". The numbers on the headdress can form a number that needs to be decomposed, and they are good friends. (For example, 2 plus 7 makes up 9; 3 and 6 make up 9, "2" and "7" are good friends, "3" and "6" are good friends. )

In teaching, properly developing some colorful games and entertaining can make students feel that learning is a relaxed and enjoyable thing, thus increasing their interest in learning. When mathematics is mixed with children's games, children feel the interest of mathematics more deeply.

Second, hands-on operation can guide students to feel and understand new knowledge and cultivate their thinking quality.

As we all know, mathematics comes from life and is applied to life. In fact, mathematics learning is also a process of abstracting from concrete things and then applying it to concrete things. In order to improve students' ability to learn mathematics, students should be allowed to discover and explore mathematical knowledge, experience the process of mathematical thinking, and apply mathematical methods and ideas in hands-on operations and activities.

1, explore in operation and think in feeling.

Operation is the main way for students to acquire knowledge, and it is also one of the effective means of teaching. Piaget said: "Knowledge itself is an activity." Action and thinking are inseparable, especially junior students, who are curious, active and willing to imitate. According to this feature, many children can say 9+4= 13 when talking about 9 plus a few, right? I provided them with 9 porn films and 4 red films, and asked them to put them on for verification. From this, there are methods such as adding ten, adding numbers, adding ideas, and treating nine as ten. Has been launched one after another. It is the teacher who provides them with the opportunity to explore actively in the operation process, and the difficult carry addition is no longer abstract and profound in front of students. Facts have proved that if students are allowed to operate, they can also become people who find their own solutions to problems.

2. Practice in operation and improve in feeling.

The new teaching goal concept has changed from emphasizing knowledge and ability to emphasizing the cultivation and infiltration of ideas and methods. Exercises can also be presented in the form of operations, so that students can improve in practice and seek differences and innovations in the process of application.

When teaching "classification", after the children initially understood and mastered the classification method, we arranged activities for students to classify pictures themselves. This activity stimulated the children's enthusiasm for thinking and made them devote themselves to their own creation. In just a few minutes, the children's performance was beyond the teacher's expectation: more than a dozen pictures were divided into different results, some by color, some by shape, some by pattern, and some by finer points. Students divide the animals in the pattern into water and land, and divide the vehicles into two wheels and four wheels. This activity is to return to specific problems after students have basically mastered the method of solving problems. Through hands-on operation, give students an opportunity to release their existing knowledge, show their learning achievements and show their personality. Through this link, students can not only consolidate their existing knowledge, but also cultivate their innovative consciousness.

In short, in junior high school mathematics teaching, improving students' learning effect is closely related to the presentation of learning content. Only by constantly presenting boring learning content in different forms that students like can we stimulate learning interest and activate subjective thinking, thus changing learning methods and improving teaching quality.